Problem: Simplify to lowest terms. $\dfrac{60}{48}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 60 and 48? $60 = 2\cdot2\cdot3\cdot5$ $48 = 2\cdot2\cdot2\cdot2\cdot3$ $\mbox{GCD}(60, 48) = 2\cdot2\cdot3 = 12$ $\dfrac{60}{48} = \dfrac{5 \cdot 12}{ 4\cdot 12}$ $\hphantom{\dfrac{60}{48}} = \dfrac{5}{4} \cdot \dfrac{12}{12}$ $\hphantom{\dfrac{60}{48}} = \dfrac{5}{4} \cdot 1$ $\hphantom{\dfrac{60}{48}} = \dfrac{5}{4}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{60}{48}= \dfrac{2\cdot30}{2\cdot24}= \dfrac{2\cdot 2\cdot15}{2\cdot 2\cdot12}= \dfrac{2\cdot 2\cdot 3\cdot5}{2\cdot 2\cdot 3\cdot4}= \dfrac{5}{4}$